Twitch.tv is a popular platform to live stream your preferred games. As only few iOS games can stream directly form the app, you can connect your device to your Mac, view your screen via QuickTime and stream it with OBS.

Open QuickTime Player and choose File > New Movie RecordingWindows users can download AirServer or Reflector

Click the arrow near the red record button and choose your device as the source camera.
You can also select your device name in the Microphone section to record any audio coming out of your iOS device.

Open OBS and under Sources click + sign and select Window Capture.

Create new one and then select your QuickTime window in the popup menu that list all your windows open.You can also add your Face Time HD Camera adding a new Video Capture Device